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What size force does the femur exerts on the kneecap if the tendons are oriented as in the figure and the tension in each tendon is 60 N?

What size force does the femur exerts on the kneecap if the tendons are oriented as in the figure and the tension in each tendon is 60 N class=

Respuesta :

 Sum of horizontal forces = 0 
F(horizontal) = 60 cos 42
                     = 44.58 

Sum of vertical forces = 0 
F(vertical) = 60 - 60 sin 42
                 = 19.85 

F = sqrt (Fh² + Fv²)
   = sqrt (44.58² + 19.85²)
   = 48.8 N
Lanuel

The size of force exerted by the femur on the kneecap is 48.81 Newton.

Given the following data:

  • Tension = 60 Newton

First of all, we would determine the horizontal component of the force acting on the kneecap.

[tex]F_y = Fcos(\theta)\\\\F_y = 60cos(42)\\\\F_y = 60 \times 0.7432\\\\F_y = 44.59 \; Newton[/tex]

For the vertical component of the force:

[tex]F_x = Fsin(\theta)\\\\ F_x = 60sin(42)\\\\ F_x = 60 \times 0.6691\\\\ F_x = 40.15\; Newton[/tex]

Next, we would find the vertical component of the net force:

[tex]\sum F_x = F - F_xsin(\theta)\\\\\sum F_x = 60 - 40.15\\\\\sum F_x = 19.85\; Newton[/tex]

Finally, the resultant force acting on the kneecap:

[tex]F_R^2 = F_y^2 + F_x^2\\\\F_R = \sqrt{F_y^2 + F_x^2} \\\\F_R = \sqrt{44.59^2 + 19.85^2}\\\\F_R = \sqrt{1988.27 + 394.02}\\\\F_R = \sqrt{2382.29}[/tex]

Resultant force = 48.81 Newton

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